Final answer:
The object of the preposition in the sentence "He saw a young woman with pink hair" is hair.
Step-by-step explanation:
The object of the preposition in the sentence "He saw a young woman with pink hair" is hair. In this sentence, the preposition is "with" and it shows the relationship between the verb "saw" and the noun phrase "a young woman." The prepositional phrase "with pink hair" describes the woman and specifies a characteristic of her appearance.